The notion of an algebra that is locally embeddable into finite dimensional algebras (LEF) and the notion of an LEF group was introduced by Gordon and Vershik in [GoVe]. M. Ziman proved in [Zi] that the group algebra of a group $G$ is an LEF algebra if and only if $G$ is an LEF group. He conjectured that an algebra generated as a vector space by a multiplicative subgroup $G$ of its invertible elements is an LEF algebra if and only if $G$ is an LEF group. In this paper we give a characterization of the invertible elements of an LEF algebra and use it to construct a counterexample to this conjecture.